The chiral logs of the K→ππ amplitude

Abstract

I calculate the leading logarithmic contributions up to two-loop order of the octet part of the K 0 → ππ amplitude. This sector of the weak chiral Lagrangian is believed to be the main source of the enhancement of the I = 0 relative to the I = 2 K 0 → ππ amplitude, the so-called ∆I = 1/2 rule. I discuss the procedure of chiral extrapolations of lattice data specific to K → ππ decays and study the implication of the present calculation on these numerically. The latter reinforces the fact that one has to expect a large enhancement of the I = 0 part of the amplitude due to re-scattering effects between the three mesons.